Trans-Series Asymptotics of Solutions to the Degenerate Painlev\'e III Equation: A Case Study
Abstract
A one-parameter family of trans-series asymptotics of solutions to the Degenerate Painlev\'e III Equation (DP3E) are parametrised in terms of the monodromy data of an associated two-by-two linear auxiliary problem via the isomonodromy deformation approach: trans-series asymptotics for the associated Hamiltonian and principal auxiliary functions and the solution of one of the sigma-forms of the DP3E are also obtained. The actions of Lie-point symmetries for the DP3E are derived.
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